A particular charge distribution is centered on the z-axis and extends from z=-∞ to z=+∞ . Its volume charge density is given by the function D p(r) = r(s+r? 3/2 where r is the radial distance from the z-axis and D and s are positive constants. Which of the following statements about this charge distribution are FALSE (select all that apply)? It has a nonzero electric dipole moment It is cylindrically symmetric The constant D and a dipole moment are expressed in the same units It is possible to use Gauss's law to calculate the electric field
![A particular charge distribution is centered on the z-axis and extends from \( z = -\infty \) to \( z = +\infty \). Its volume charge density is given by the function
\[
\rho(r) = \frac{D}{r(s + r^2)^{3/2}}
\]
where \( r \) is the radial distance from the z-axis and \( D \) and \( s \) are positive constants.
Which of the following statements about this charge distribution are FALSE (select all that apply)?
- [ ] It has a nonzero electric dipole moment
- [ ] It is cylindrically symmetric
- [ ] The constant \( D \) and a dipole moment are expressed in the same units
- [ ] It is possible to use Gauss's law to calculate the electric field generated by this charge distribution](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe09d4462-f34d-4530-ac40-5ce52271c7b7%2F02ea2911-4318-433d-b5af-b8455185d110%2Fm97pxrp_processed.png&w=3840&q=75)
For both positive and negative values of r, the volume charge density is the same as the opposite sign, so it has zero electric dipole moment.
The unit of constant D and dipole moment is the same because the denominator of the volume charge density unit is m4. The unit of volume charge density is C/m3. Hence, to make a volume charge density unit, the constant D unit should be C-m, which is a dipole moment unit.
It is cylindrically symmetric because along the z-axis there is charge distribution is fixed and at any point at radial distance r from the z-axis, the volume charge density is also fixed.
Gauss law is used for the closed surface to determine the electric field, so, it is possible to use Gauss's law to calculate the electric field generated by this charge distribution.
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